2.10 Activity

Split a segment into 2 equal pieces by constructing the perpendicular bisector.
Follow the steps below to construct a perpendicular bisector.[br][br]1) Use "Compass" to construct a circle with radius AB centered at A.[br]2) Use "Compass" to construct a circle with radius AB centered at B.[br]3) Use "Intersect" to mark the points of intersection of the two circles.[br]4) Use "Line" to draw a line through those two points.[br]5) Use "Intersect" to mark the point where the line intersects segment AB.[br][br]*Optional - Measure your 2 segments to verify that they are equal.
Split segment AB into 2 equal pieces.
Below are the steps for constructing a perpendicular bisector. Follow these steps again to split segment AB into 2 equal parts. THEN, split those two segments into 2 equal parts.[br][br][b]*Hint: You will do 3 perpendicular bisector constructions here.[br][/b][br]1) Use "Compass" to construct a circle with radius AB centered at A.[br]2) Use "Compass" to construct a circle with radius AB centered at B.[br]3) Use "Intersect" to mark the points of intersection of the two circles.[br]4) Use "Line" to draw a line through those two points.[br]5) Use "Intersect" to mark the point where the line intersects segment AB.[br][br]*Optional - Measure your 2 segments to verify that they are equal.
Split segment AB into 4 equal pieces.
How can we split a segment into 3 equal pieces using dilations?!
Follow the steps below to split a segment into 3 (or any number of) pieces.[br][br]1) Construct a line parallel to the segment (ALREADY DONE FOR YOU).[br]2) Mark point C so that it is to the left of point A (ALREADY DONE FOR YOU).[br]3) From point C use "Compass" to mark off equal segments (ALREADY DONE FOR YOU).[br][br]*You can use "Compass" to add more points here if you like. They must all have radius set to CD. [br]**Important: The last point on line CD must be to the right of point B.[br][br]4) Use "Ray" to construct ray CA.[br]5) Use "Ray" to contruct ray FB. (or from whatever your rightmost point is)[br][br]6) Use "Intersect" to mark the point where these rays intersect. This is the center of dilation.[br][br]7) Use "Ray" to construct rays from the remaining points on line CD to the center of dilation.[br][br]8) Use "Intersect" to mark the points where each ray intersects segment AB.[br][br]Your segment AB has now been split into 3 or more equal pieces. Use "Distance or length" to verify that they are equal.[br][br]
Split segment AB into 3 equal pieces. (Line CD is parallel to AB)

Information: 2.10 Activity